Solution Dilution Math: C1V1 = C2V2 and When It Does Not Apply

The dilution equation C1V1 = C2V2 is one of the most widely used formulas in science and industry. Laboratories, pharmacies, cleaning product manufacturing, agriculture, and food processing all rely on it daily. And while the formula itself is simple, the application has more pitfalls than most people expect. The formula and what it means C1V1 = C2V2 C1 = initial concentration V1 = initial volume (the volume of concentrated solution you need) C2 = final (desired) concentration V2 = final (desired) total volume You are solving for V1: how much of the concentrated stock solution do you need to make your desired dilution. V1 = (C2 x V2) / C1 Example: You have a 10% bleach solution and need to make 500 mL of a 0.5% solution. V1 = (0.005 x 500) / 0.10 = 25 mL Take 25 mL of the 10% solution and add water to bring the total volume to 500 mL (add 475 mL of water). When C1V1 = C2V2 does not work This formula assumes the solute and solvent volumes are additive. For dilute aqueous solutions, this